Not the greatest agreement but someone with a better grasp of statistics could easily say whether the latter estimat is really different from 4600 at a high confidence level...

John, I'm enjoying reading what you've dug up for the sextant numbers. I'm not very accomplished in the realm of statistics, but reading your latest made me think of the German Tank Problem, a famous use of statistical analysis of serial numbers of captured German tanks during WWII that led to an accurate estimate of German tank production numbers. Perhaps there's something from that analysis of serial numbers that you can exploit.

Another installment in the Naval Observatory sextant number story. In trying to come up with a chronology of issuance of Naval Observatory (N.O.) numbers to sextants based on the USNO Annual Reports for 1916-1930, one question I wondered about was when the assignment of N.O. numbers to sextants began. Some Googling led me to a book sold through Amazon containing a collection of the USNO Annual Reports from 1884 to 1900, which I ordered and just received this afternoon. The Annual Report for 1884 contains this statement, apparently from the superintendent of the observatory:

“An effort as been made at the Observatory to establish a system by which all sextants and octants for issue to the Navy shall be examined and corrected, as far as practicable, and their errors, as well as those of the instruments used for meteorological observations be furnished to the navigators of vessels from this place so that there would be a continuous record of every instrument supplied by the Bureau of Navigation. I recommend that all instruments found to be worthless be broken up, in order that they be rendered incapable of doing harm to any one…”

From this, it seems like 1884 marked the start of the assignment of N.O. numbers to instruments inspected at the Observatory. And sure enough, the USNO Annual Report for 1886 contains the only actual discussion of the assignment of N.O. numbers to instruments in any of the USNO reports I’ve read, and I’ve read through the whole pdf of 1916-1930 Annual Reports and some from the 1904-1913 period, as well.

The discussion of assigning N.O. numbers in the ’86 report isn’t in a section devoted to sextants, however, it’s in a discussion about the testing of thermometers:

“…The thermometer is marked on its stem with the hall mark (shown in the annexed cut) and with the Observatory number by means of a writing diamond. A certificate, such as that which follows, is sent with the thermometer when issued or returned after being tested”.

A jpg showing this part of text and the example certificate, N.O. #66 is attached.

I noted in a previous post that a few USN chronometers/torpedo boat watches apparently were assigned N.O. numbers; whether there was a single set of numbers for different types of instruments, or parallel sets of numbers for different types, I don’t know.

Note added: I've gone through my 1884-1900 USNO Annual Report Collection and I count a total of 287 clinical thermometers for hospitals certified at the Naval Observatory, all between 1886 and 1888; there is no mention of clinical thermometers after 1888. Also, I looked at all the chronometer trials results listed from 1884-1900 and see no chronometers having N.O. numbers; the 16 'old' chronometers with N.O. numbers tested in 1920 (see in reply #100 above) remain the only ones I've come across.

Why does any of this matter? The reason is that we’d like to know what year the Naval Observatory stamped a sextant with N.O. number 1542. If the Naval Observatory started stamping N.O. number into sextants shortly before WWI, then from the information published in the 1916-1930 USNO Annual Reports, I would think (see my earlier posts on this thread and on this other thread) that sexant #1542 was a WWI-era sextant and probably left the USN either by transfer to the merchant marine or by sale as surplus equipment some time probably after 1928. But it looks as if the observatory started marking sextants with N.O. numbers well before 1900, making it conceivable that sextant #1542 saw action in the Spanish-American war, say. The 1884-1900 Annual Reports also say that unwanted equipment was disposed of on several occasions during this period, so there would have been plenty of opportunities for one of these sextants to make its way to Gardner Island with Thurston Howell the first.

From what I’ve seen so far of the pre-1916 reports, the number of sextants that could have been assigned N.O. numbers probably got no where near 1500, or even 500; we also have clues about the chronology of issuance of N.O. numbers from the dated eccentricity certificates of sextants that are in museum collections or that have turned up on ebay. All the same, the story coming out of the 1884-1900 USNO Annual Reports makes the job of coming up with a chronology of issuance of N.O. numbers to sextants more uncertain.

John, I'm enjoying reading what you've dug up for the sextant numbers. I'm not very accomplished in the realm of statistics, but reading your latest made me think of the German Tank Problem, a famous use of statistical analysis of serial numbers of captured German tanks during WWII that led to an accurate estimate of German tank production numbers. Perhaps there's something from that analysis of serial numbers that you can exploit.

Bruce,

I'd never heard of the German Tank Problem. Thanks for the link, it made for interesting reading.

To my statistically untrained eyes, the distribution of N.O. numbers in the chart in reply #98 looks very non-random. Thinking about the first six rows as the six sides of a die, what are the chances that after 50 rolls there'd be no fours (i.e., no 3000-3999s)? I think the answer is (5/6) raised to the 50th power, which (I think) comes out to less than 1/10,000. Or maybe I blew my calculator's mind by raising to the 50th power ...

I'm no longer worried that I'm making Ric's head spin because I'm making my own head spin.

In Reply #100 above I mentioned that a table of torpedo boat watch trials in a USNO Annual Report (the table is for trials performed in 1920) lists about 16 T.B.W. watches having USNO numbers, all in the 4000s to 5000s. Tonight a little Googling led me to a Horology web site which shows nice photos of several other chronometers/T.B.W.s that have N.O. numbers, also in the 4000s. It appears that a great deal is known about the production of these watches, e.g. manufacturer's serial numbers can be used to pin down date of manufacture. A December 29 posts on that thread mentions a book by Marvin Whitney who was a USNO watchmaker. According to the December 29 post, Whitney's book says that a pair of Longines T.B.W.s were tested and accepted by the U.S. Naval Observatory in 1913 and given Naval Observatory serial numbers 4,019 and 4,054 respectively. If true, and there weren't parallel N.O. number lists for Sextants and chronometers, then the sextant with N.O. number 1542 would appear to have been produced before 1913, perhaps well before 1913. Hello Thurston Howell the first!

----------added note: None of the four N.O. numbers of TBWs at the horology web site (4434 for the nice shiny TBW in the picture, Whitney's 4019 and 4054, and 4462 which is at the link given in the 12/29/2011 20:22 post) on the horology site match any of the N.O. numbers in the Ameliapedia sextant list; neither did any of the 16 TBWs I found in the USNO Annual Report Table for 1920...--------Another note: A January 3 post from the owner of TBW #4434 indicates it was manufactured after 1910 and invoices to the US Longines distributor in 1919. So, 4019 and 4054 appear to be 1913 dates and 4434 a 1919 date?And to make my head spin even faster, the other watch linked to in the 12-29 20:22 post has a USNO number of 1927256; not date information for that watch. I'm guessing for some reason the USNO engraved this watch with its manufacturer's number...

------------One key point to keep in mind when looking at the N.O. numbers of TBWs is whether the watch mechanism is in its original case. It would be good to know the manufacturer's number of the mechanism. It would also be great to have readable copies of all the USNO chronometer trial tables which generally report manufacturer's numbers. All the tables in the 1884-1900 collection that can be downloaded for free at Forgotten Books are legible, but from 1900 onwards the tables in the USNO annual reports I've gotten from Google were generally badly copied and unreadable.

Finding the dates of Torpedo Boat Watches or other USN chronometers that closely bound N.O. number 1542 seems like a good way to date the initial appearance of sextant #1542 at the Naval Observatory. TBWs of interest might show up on eBay, watch dealers, etc. but from what I've been reading the information provided by such vendors may in some cases be suspect. I would think the best way to really pin down what naval chronometers can tell us about the dating of sextant 1542 would be to contact the National Association of Watch and Clock Collectors or some other such organization. Watch and clock collectors have apparently amassed a lot of good information from company records on dates of manufacture, sales to the government, etc. The link I provided above provides a brief history of the deck watch aka Torpedo Boat Watch suggesting that USN interest in these began in the 1890s. Page 48 of the 1904 USNO Annual Report tells us that the USN was at that date purchasing TBWs from foreign sources only and thus planning to conduct a TBW trial in part to encourage US manufacturers to begin producing a model of sufficient quality for USN needs.

----------Perhaps this fellow who gave a talk titled “Hamilton Military Timepieces of WWI and WWII” at a NAWCC regional meeting in the Pacific Northwest would be worth contacting...

Here on ebay is another Torpedo Boat Watch with a USNO number (#4308) on the case and Longines number 298008 on the movement. I think it is prudent to consider the possibility that the case may have held a different mechanism at the time it received its USNO number. I looked through the few legible chronometer trial tables in the USNO annual reports and couldn't find a Longines with this manufacturer number. The table at this site the manufacturer's number indicates an approximate manufacture date of 1912-1913. But how accurate this table is I don't know...

This Popular Astronomy article on the U.S.N.O.'s observation of the solar eclipse of 1918 at Baker, Ore. indicates a Brandis Sextant with (N.O. or mfgr.?) number 3257 along with Nardin Siderial Break Circuit Chronometers 1518 and 1902; also used was a Nardin Mean Time Break chronometer numbered 589 and a Hamilton Mean Time Watch identified as 'USN 1758'.

Would anybody care to hazard a guess as to how many sextants the USN might have needed pre-WWI and at its peak size during the war?...Same question for the U.S. merchant fleet?...

The attached jpg shows a chart indicating the size of the pre-war USN and post-1914 additions from this web site.

I wonder if a USN ship's logbooks would indicate the N.O. numbers of the sextants it was using to navigate with. I looked at the excerpt from the Colorado's deck log and that didn't look too promising but it might be worth slogging through the logs of a ~1914 era USN vessel just to see what is there...

It’s funny where my efforts to figure out the chronology of issue of Naval Observatory numbers have taken me. First, it was eccentricity testing at the Naval Observatory, then it was on to the wonderful world of torpedo boat watches, then a brief aside to the total solar eclipse of 1918. I thought today I’d be getting back to torpedo boat watches, but instead I’m back on the sextant beat, the Keffel & Esser sextant beat, that is.

As an aside, I’d forgotten until today that my personal history intertwines ever so slightly with that of the Keuffel & Esser company. I live in New York City and for years I had gone by and admired the fine old Keuffel & Esser building near the waterfront on Fulton Street in Manhattan; Brandis at one time had a location in this same area, and our old friend Fred Noonan lived a short distance away, at 25 South Street, in and around 1918.

Now, back to the story. Keuffel and Esser made things besides sextants, things like surveying equipment. And just like there are collectors of old watches, there are collectors of old surveying equipment. And collectors of old surveying equipment apparently have their serial number charts to date the stuff they buy, just like collectors of old watches do. So, here is a table of Keuffel and Esser serial numbers with manufacture dates from Surveying Antiques.com.

There are four Keuffel & Esser sextants in the Ameliapedia sextant table with Naval Observatory numbers. In the table below I list the N.O. number, K&E serial number, date of manufacture as indicated by the table from Surveying Antiques, and date of the eccentricity certificate we have for the sextant. The last sextant in the table is the sextant that I mentioned in reply #99, whose N.O. number we don't have .

The dates of manufacture would of course be the earliest the sextants could have appeared at the Naval Observatory, while the eccentricity certificate dates may represent re-certifications rather that the first certification of the sextant.

The K&E sextant with an N.O. number 1555 is only a few removed from our holy grail sextant, N.O. #1542; if we have a correct date for the K&E sextant then it would seem that the sextant with N.O. #1542 passed through the Naval Observatory for the first time in 1918 or 1919. It is interesting to note that the Ludolph sextant that Noonan gave to a fellow Pan Am pilot, has a manufacture date of 1919 (as indicated by the Roman numerals XIX).

------It would be nice to find more K&E sextants with N.O. numbers and eccentricity certificates and see how well they can be dated using the table in SurveyingAntiques.com. Also, I'm aware the order of dates of the first 3 sextants don't quite jibe with the order of their N.O. numbers, but all the same I think this table is worth thinking about...-------

There are four Keuffel & Esser sextants in the Ameliapedia sextant table with Naval Observatory numbers. In the table below I list the N.O. number, K&E serial number, date of manufacture as indicated by the table from Surveying Antiques, and date of the eccentricity certificate we have for the sextant. The last sextant in the table is the sextant that I mentioned in reply #99, whose N.O. number we don't have .

The dates of manufacture would of course be the earliest the sextants could have appeared at the Naval Observatory, while the eccentricity certificate dates may represent re-certifications rather that the first certification of the sextant.

The K&E sextant with an N.O. number 1555 is only a few removed from our holy grail sextant, N.O. #1542; if we have a correct date for the K&E sextant then it would seem that the sextant with N.O. #1542 passed through the Naval Observatory for the first time in 1918 or 1919. It is interesting to note that the Ludolph sextant that Noonan gave to a fellow Pan Am pilot, has a 1919 manufacture 1919 (as indicated by the Roman numerals XIX).

Fascinating.

I'll try to expand the Ameliapedia article tomorrow morning--oh, no, I mean, later this same morning!--unless Bruce beats me to it.

If the K&E folks have tables like that, maybe some Brandis collectors do, too.

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